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http://hdl.handle.net/20.500.12358/21357
TitleOn Codes over the Rings Fq + uFq + vFq + uvFq
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Abstract

Codes over finite rings have been studied in the early 1970’s [4]. A great deal of attention has been given to codes over finite rings from 1990 [20], because of their new role in algebraic coding theory and their successful applications. In previous studies, some authors determined the structure of the ring F2 + uF2 + vF2 + uvF2, where u2 = v2 = 0 and uv = vu, also they obtained linear codes, self dual codes, cyclic codes, and consta-cyclic codes over this ring as in [24],[25],[26],[27]. In this thesis, we aim to generalize the previous studies from the ring F2+uF2+vF2+uvF2 to the ring Fq + uFq + vFq + uvFq, where q is a power of the prime p and u2 = v2 = 0 uv = vu, so we obtain the linear codes over R = Fq + uFq + vFq + uvFq, then we investigate self dual codes over R and we find that it can be generalized only when q is a power of the prime 2, also we obtain cyclic and consta-cyclic codes over R, and we generalize the Gray map used for codes over F2 + uF2 + vF2 + uvF2, finally we obtain another gray map for codes over R.

Authors
Yaghi, Ibrahim M.
Supervisors
Al-ashker, Mohammed M.
Typeرسالة ماجستير
Date2013
LanguageEnglish
Publisherالجامعة الإسلامية - غزة
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  • PhD and MSc Theses- Faculty of Science [445]
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The institutional repository of the Islamic University of Gaza was established as part of the ROMOR project that has been co-funded with support from the European Commission under the ERASMUS + European programme. This publication reflects the views only of the author, and the Commission cannot be held responsible for any use which may be made of the information contained therein.

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The institutional repository of the Islamic University of Gaza was established as part of the ROMOR project that has been co-funded with support from the European Commission under the ERASMUS + European programme. This publication reflects the views only of the author, and the Commission cannot be held responsible for any use which may be made of the information contained therein.

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